The Euler class of planar groups

TL;DR

This paper provides a comprehensive homological classification of how surface groups act on the plane across various smoothness levels, enhancing understanding of their topological and geometric properties.

Contribution

It offers a detailed exposition of the homological classification of surface group actions on the plane, covering all degrees of smoothness, which was previously not fully understood.

Findings

Complete classification of surface group actions on the plane

Extension of classification across all smoothness degrees

Deeper insight into topological and geometric properties

Abstract

This is an exposition of the homological classification of actions of surface groups on the plane, in every degree of smoothness.